Computational Modeling of Organic Fluor Molecules

Transcription

1 Clemson University TigerPrints All Theses Theses Computational Modeling of Organic Fluor Molecules Nathaniel Jacob Nichols Clemson University, Follow this and additional works at: Recommended Citation Nichols, Nathaniel Jacob, "Computational Modeling of Organic Fluor Molecules" (2017). All Theses This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact

2 COMPUTATIONAL MODELING OF ORGANIC FLUOR MOLECULES A Thesis Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Master of Science Environmental Engineering by Nathaniel Jacob Nichols May 2017 Accepted by: Dr. Lindsay Shuller Nickles, Committee Chair Dr. Timothy DeVol Dr. Ayman Seliman

3 ABSTRACT The goal of this research is to benchmark the computational parameters necessary to accurately model the fluorescence process of seven organic scintillating molecules, including 2 (1 naphthyl) 5 phenyloxazole (αnpo), 2 (1 naphthyl) 4 vinyl 5 phenyloxazole (vnpo), 5 (4 Bromophenyl) 3 (4 ethylphenyl) 1 phenyl 4,5 dihydro 1H pyrazole (PZ1), 3 (4 Ethylphenyl) 5 (4 vinylphenyl) 1 phenyl 4,5 dihydro 1H pyrazole (vpz1), 3 (4 Ethylphenyl) 5 (4 fluorophenyl) 1 phenyl 4,5 dihydro 1H pyrazole (PZ2), 2 (4 tert butylphenyl) 5 (4 biphenylyl) 1,3,4 oxadiazole (PBD), and 2 [4 (4 vinylbiphenylyl)] 5 (4 tert butylphenyl) 1,3,4 oxadiazole monomer (vpbd). Organic fluorophores are utilized for scintillation detection, as the fluorophores emit detectable photons in response to energy deposition from ionizing radiation into the scintillator. Optimal detection efficiency occurs with emitted photons at the maximum response wavelength of the photodetector, which, for a conventional photomultiplier tube, is 420 nm. Identifying an optimal organic fluorophore structure through synthesis is expensive. Instead, time dependent density functional theory (TD DFT) can be used to predict absorption and emission wavelengths for optimal fluor structures. We report on the performance of four exchange correlation energy functionals (B3LYP, M06 2X, CAM B3LYP, wb97x D) for each fluor molecule in toluene and cyclohexane solutions as implemented in the polarizable continuum model (PCM). This research has identified the M06 2X functional as the best functional for identifying distinct absorption and emission features throughout the entire corresponding spectra for the molecules of interest. Furthermore, the work presented here has determined that the 6 31G(d,p) basis set in combination with the M06 2X functional produce computational results that follow general trends produced in experimental measurements of absorption and emission wavelengths. ii

4 Methods for explicitly modeling solvation were developed and compared with calculations performed within the PCM framework (i.e., implicit solvation). iii

5 AKNOWLDEGEMENTS I would first like to thank my advisor, Dr. Shuller Nickles of the Environmental Engineering and Earth Sciences Department at Clemson University. Dr. Shuller Nickles has provided exemplary guidance during my time at Clemson University. She has always been available for answering my questions and for steering me in the right direction while allowing this work to remain my own. I would also like to thank my research committee members, Dr. DeVol and Dr. Seliman of the Environmental Engineering and Earth Sciences Department at Clemson University. Dr. DeVol and Dr. Seliman were outstanding committee members, keeping in constant communication with my work and offering technical insight to the experimental systems I modeled. Finally, I must express profound gratitude to both of my parents for providing me unwavering support throughout my studies and research, which has ultimately lead me to the writing of this thesis. This accomplishment would not be possible without you. iv

6 TABLE OF CONTENTS PAGE COMPUTATIONAL MODELING OF ORGANIC FLUOR MOLECULES... i ABSTRACT... ii AKNOWLDEGEMENTS... iv LIST OF TABLES... vi LIST OF FIGURES... vii LIST OF ABBREVIATIONS... ix 1. INTRODUCTION THEORY PHYSICAL PROCESS COMPUTATIONAL METHODS CHEMICAL STRUCTURES METHODOLOGY GAS PHASE MODEL IMPLICIT SOLVATION MODEL HYBRID SOLVATION MODEL RESULTS ENERGY FUNCTIONAL EFFECTS IMPACT OF SOLVATION CHEMICAL EFFECTS CONCLUSION APPENDIX 1: SUPPLEMENTARY FIGURES AND TABLES REFERENCES v

7 LIST OF TABLES TABLE PAGE Table 1. Donor and Acceptor Orbitals and Corresponding Interaction Energies (kcal/mol) of the vnpo Fluor Molecule Calculated Using B3LYP/6 31G(d,p) and M06 2X/6 31G(d,p) Energy Functionals in Toluene Table 2. Calculated HOMO, LUMO, HOMO LUMO Gap, and Optical Gap Energies Using B3LYP/6 31G(d,p) and M06 2X/6 31G(d,p) in Toluene Table 3. Comparison of Bonding Order Between the HOMO and LUMO States Calculated Using B3LYP and M06 2X Functionals Table 4. The Absorption and Emission Wavelengths λ (nm), Oscillator Strengths (f), and Stokes Shifts Δν (cm 1 ) of Gas Phase Linear Response (Gas Phase), PCM Linear Response (PCM LR) in Toluene, and PCM State Specific (PCM SS) in Toluene for Each Fluor Molecule Using M06 2X/6 31G(d,p) Table 5. Percent Differences of the Intensities of the Three Most Prominent Absorption Transitions, Their Corresponding Wavenumber (λ), and the Emission Peaks from the First Excited State of Each Fluor Molecule in Toluene and Cyclohexane Solutions using M06 2X/6 31G(d,p) Table 6. Absorption and Emission Wavelengths λ (nm), Oscillator Strengths f, and Stokes Shifts Δν (cm 1 ) of αnpo and vnpo Fluor Molecules Calculated by Hybrid Solvation and the PCM SS Method Using M06 2X/6 31G(d,p) in Toluene Table 7. Calculated HOMO, LUMO, HOMO LUMO Gap, and Optical Gap Energies (ev) of Each Fluor Molecule in Toluene Using M06 2X/6 31G(d,p) Table 8. Comparison Between Experimental Oscillator Strengths (f E ) and Calculated Oscillator Strengths (f C ) Using M06 2X/6 31G(d,p) Table 9. Absorption and Emission Wavelengths λ (nm), and Stokes Shifts Δν (cm 1 ) of Each Fluor Molecule Calculated by the PCM SS and PCM Hybrid M06 2X/6 31G(d,p) Scheme and the Corresponding Experimental Values in Toluene Table 10. Absorption and Emission Wavelengths λ (nm), Oscillator Strengths f, and Stokes Shifts Δν (cm 1 ) of Each Fluor Molecule Calculated by the PCM SS Method Using M06 2X/6 31G(d,p) vi

8 LIST OF FIGURES FIGURE PAGE Figure 1. Jablonski Diagram demonstrating the fluorescence process, where GS is the ground state, S1 and S2 are singlet excited states Figure 2. Chemical structures of αnpo and vnpo Figure 3. Chemical structures of PBD and vpbd Figure 4. Chemical structure of PZ1, vpz1, and PZ Figure 5. Flow diagram of computational steps required to complete the gas phase absorption and emission calculations. DFT theory (solid box), TD DFT (dashed box) Figure 6. Flow diagram of computational steps required to complete the geometry optimization, absorption, and emission calculations for PCM solvation implementation. DFT theory (solid box), TD DFT (dashed box) Figure 7. PCM hybrid technique showing the initial coordination of a single explicit toluene for a) αnpo and b) vnpo Figure 8. Two layer ONIOM technique for αnpo in toluene. M06 2X/6 31G(d,p) theory is applied to the fluor molecule, HF/6 31G(d,p) theory for interactions between the fluor molecule and explicit toluene molecules, and ONIOMPCM theory to model bulk solvation Figure 9. Absorption spectra for αnpo in toluene for each functional in toluene. Curves normalized to CAM B3LYP Figure 10. Calculated vnpo absorption spectra in toluene vs experimental spectra in methyl acetate. Calculated curves normalized to wb97x D, experimental curve normalized to itself Figure 11. HOMO and LUMO molecular orbitals of αnpo for B3LYP and M06 2X in toluene Figure 12. First excited state absorption peak location for each fluor molecule in cyclohexane and toluene, using M06 2X/6 31G(d,p). *No data available Figure 13. αnpo absorption (solid) and emission (dashed) spectra in chloroform, cyclohexane, diethyl ether, and toluene using M06 2X/6 31G(d,p). Spectra normalized to emission spectrum of diethyl ether Figure 14. vnpo absorption (solid) and emission (dashed) spectra in chloroform, cyclohexane, diethyl ether, and toluene using M06 2X/6 31G(d,p). Spectra normalized to emission spectrum of diethyl ether Figure 15. PZ1 absorption (solid) and emission (dashed) spectra in chloroform, cyclohexane, diethyl ether, and toluene using M06 2X/6 31G(d,p). Spectra normalized to absorption spectrum of diethyl ether Figure 16. Absorption spectra for αnpo with PCM SS, hybrid solvation using PCM hybrid, and ONIOM two layer with static fluor and static toluene approximations. Spectra normalized to PCM SS spectrum vii

9 LIST OF FIGURES (CONTINUED) FIGURE PAGE Figure 17. Absorption spectra for vnpo with PCM SS, hybrid solvation using PCM hybrid, and ONIOM two layer with static fluor and static toluene approximations. Spectra normalized to PCM SS spectrum Figure 18. αnpo absorption (solid line) and emission (dashed) spectra calculated using implicit PCM and PCM hybrid models and M06 2X/6 31G(d,p). Spectra normalized to PCM emission Figure 19. vnpo absorption (solid line) and emission (dashed) spectra calculated using implicit PCM and PCM hybrid models and M06 2X/6 31G(d,p). Spectra normalized to PCM emission Figure 20. Top: Calculated absorption spectra of each fluor molecule using the PCM state specific model in toluene and M06 2X/6 31G(d,p). Spectra normalized to calculated vpbd spectra. Bottom: Experimental absorption spectra of each fluor molecule in methyl acetate. Spectra normalized to experimental vpbd spectra Figure 21. HOMO and LUMO molecular orbitals of αnpo and vnpo in toluene Figure 22. HOMO and LUMO molecular orbitals of PBD and vpbd in toluene Figure 23. HOMO and LUMO molecular orbitals of PZ1, vpz1, and PZ2 in toluene Figure 24. Emission spectra in toluene using M06 2X. Curves normalized to vpbd Figure 25. Comparison between experimental oscillator strengths (f E ), calculated oscillator strengths (f C ) using M06 2X/6 31G(d,p) Figure 26. Absorption and emission wavelengths λ (nm), and Stokes Shifts (nm) of each fluor molecule calculated by the PCM SS M06 2X/6 31G(d,p) scheme and the corresponding experimental values Figure 27. Calculated αnpo absorption spectra (left) and emission spectra (right) for each functional in toluene. Spectra normalized to CAM B3LYP Figure 28. Calculated vnpo absorption spectra (left) and emission spectra (right) for each functional in toluene. Spectra normalized to wb97x D Figure 29. Calculated PBD absorption spectra (left) and emission spectra (right) for each functional in toluene. Spectra normalized to M06 2X Figure 30. Calculated vpbd absorption spectra (left) and emission spectra (right) for each functional in toluene. Spectra normalized to wb97x D Figure 31. Calculated PZ1 absorption spectra (left) and emission spectra (right) for each functional in toluene. Spectra normalized to wb97x D Figure 32. vpz1 absorption spectra (left) and emission spectra (right) for each functional in toluene. Absorption spectra normalized to wb97x D. Emission spectra normalized to B3LYP Figure 33. PZ2 absorption spectra for each functional in toluene. Spectra normalized to wb97x D viii

10 LIST OF ABBREVIATIONS αnpo DFT ES GGA GS GTO HOMO LDA LDSA LR LUMO meta GGA ONIOM PCM PBD PZ1 PZ2 STO SS TD DFT vnpo vpbd vpz1 2 (1 naphthyl) 5 phenyloxazole Density Functional Theory Excited State Generalized Gradient Approximation Ground State Gaussian type orbitals Highest occupied molecular orbital Local Density Approximation Local Spin Density Approximation Linear Response Lowest unoccupied molecular orbital Meta Generalized Gradient Approximation our own N layered integrated molecular orbital + molecular mechanics Polarizable Continuum Model 2 (4 tert butylphenyl) 5 (4 biphenylyl) 1,3,4 oxadiazole 5 (4 Bromophenyl) 3 (4 ethylphenyl) 1 phenyl 4,5 dihydro 1H pyrazole 3 (4 Ethylphenyl) 5 (4 fluorophenyl) 1 phenyl 4,5 dihydro 1H pyrazole Slater type orbitals State Specific Time Dependent Density Functional Theory 2 (1 naphthyl) 4 vinyl 5 phenyloxazole 2 [4 (4 vinylbiphenylyl)] 5 (4 tert butylphenyl) 1,3,4 oxadiazole monomer 3 (4 Ethylphenyl) 5 (4 vinylphenyl) 1 phenyl 4,5 dihydro 1H pyrazole ix

11 1. INTRODUCTION The use of organic fluorescent materials for scintillation counting has grown in the fields of physics, chemistry and biology 3, 4. The discipline of Health Physics relies on scintillation counting for radiation detection purposes. Common inorganic scintillators are employed in the field of radiation detection, such as sodium iodide, but require a crystalline lattice to enable to scintillating process. The fluorescence process in organic scintillators occurs from the energy transitions of a single molecule, and can therefore be observed from a molecular species independent of its physical state 5. These organic scintillators can take the form of single crystals, plastics, or liquids. Fluorophores constructed as single crystals represent the fluorophores in their purest form, while the plastic and liquid forms of these scintillators have the fluorophores dissolved in an organic solvent 5. Organic fluorophores with absorption spectra within the UV or near UV region of light are appropriate for the detection of gamma rays, alpha and beta particles, as well as fast neutrons 6. A multitude of processes must occur in order to measure a radiological count with an organic fluor dissolved in an organic solvent. Incoming particulate radiation will first interact with the solvent matrix. The kinetic energy from the incident radiation will be fully absorbed by the solvent matrix and transferred via phonon phonon interactions to the organic fluor. The solvent is selected such that it efficiently transfers energy to the organic fluor to ensure the highest detection efficiency. Once the energy is transferred to the organic fluor molecule, an electronic excitation and de excitation occurs, producing a photon in the visible range of light. This absorption of energy and emission of a photon by the singlet states of the organic fluor is called fluorescence and is paramount in radiation detection, as the photons detected represent radiation interactions in the sample. Photomultiplier tubes collect the emitted photons and have a peak efficiency for photon wavelengths around 420 nm. 1

12 Recently, Seliman et al. synthesized 2 (1 naphthyl) 4 vinyl 5 phenyloxazole (vnpo) from 2 (1 naphthyl) 5 phenyloxazole (αnpo), and 2 [4 (4 vinylbiphenylyl)] 5 (4 tert butylphenyl) 1,3,4 oxadiazole monomer (vpbd) from 2 (4 tert butylphenyl) 5 (4 biphenylyl) 1,3,4 oxadiazole (PBD)) 1. Similarly, Bliznyuk et al. presented the synthesis of 5 (4 Bromophenyl) 3 (4 ethylphenyl) 1 phenyl 4,5 dihydro 1H pyrazole (PZ1), 3 (4 Ethylphenyl) 5 (4 vinylphenyl) 1 phenyl 4,5 dihydro 1H pyrazole (vpz1), and 3 (4 Ethylphenyl) 5 (4 fluorophenyl) 1 phenyl 4,5 dihydro 1Hpyrazole (PZ2) as viable organic fluors 2. While experimental results are strong indicators of performance, the synthesis of new organic molecules in search of an ideal fluorophore is costly. Instead, modeling the fluorescent properties of organic fluorophores enable the prediction of optimal organic molecular photo physics. Quantum mechanical calculations can be used to predict ground state geometries, was well as excited state geometries and the associated excited state energetic transitions. Density Functional Theory (DFT) and Time Dependent Density Functional Theory (TD DFT) are popular computational methods used to model the electronic excitation of a molecule from its ground state 7. DFT and TD DFT are not new theories, and recently there have been numerous studies that investigate the photo physical behavior of organic compounds Calculated absorption and emission wavelengths of the organic fluors are compared with experimental measurements to determine the appropriate computational parameters for future predictive calculations. This study will examine seven different organic molecules including αnpo, vnpo, PBD, vpbd, PZ1, vpz1, and PZ2. The TD DFT calculations were executed using the 6 31G(d,p) basis set with four different energy functionals, (B3LYP, M06 2X, CAM B3LYP, wb97x D), in both toluene and cyclohexane solvents within the PCM framework. Solvents of diethyl ether and chloroform were also included for the αnpo, vnpo, and PZ1 fluors within the PCM framework 2

13 in order to compare the effects of organic solvents with larger dielectric constants. Solute solvent interactions were modeled using both the polarizable continuum model (PCM) and a three hybrid implicit/explicit models for the αnpo and vnpo fluor molecules. 2. THEORY 2.1 PHYSICAL PROCESS Figure 1 displays a Jablonski diagram, which illustrates the physical process an electron undergoes during a fluorescent event. Figure 1. Jablonski Diagram demonstrating the fluorescence process, where GS is the ground state, S1 and S2 are singlet excited states. In the case of an organic scintillator, an electron is first excited by energy transferred to the organic fluor from the solvent. The electron can be excited into any of the singlet excited states, marked S1 and S2. If an electron is excited to a state higher than S1, it will de excite to the S1 state in picoseconds through radiationless internal conversion 5. If the electron has excess vibrational energy (i.e., not in thermal equilibrium with its surroundings), the electron will undergo a radiationless relaxation to the lowest S1 state. The electron in the lowest S1 state will 3

14 undergo prompt fluorescence down to one of the various GS levels on a time scale of a few nanoseconds 5. Figure 1 also shows that the up arrows designating absorption are greater than or equal to the down arrows designating fluorescence, which corresponds to the lower amount of energy lost in emission than the energy gained absorbed during excitation, leading to a redshift of photon light COMPUTATIONAL METHODS Fluorescence can be calculated by approximating the solution to the time dependent Schrödinger equation:, Ψ r,t, Ψ r,t...(1) Where is the Hamiltonian, Ψ is the electron wave function, and E is the total electron binding energy of the system. The Schrödinger equation can be solved exactly for a single body system (e.g., a hydrogen atom); however, an exact solution the N body Schrödinger equation does not exist. Density functional theory (DFT) was developed to solve the Schrödinger equation using the basis sets and energy functionals to develop the electron density as an approximation for the wave function 7. Appendix 2 provides a thorough explanation of the quantum mechanical theory behind the computational methods used in this study. Basis sets are a collection of functions (e.g., Gaussian functions) used to approximate the atomic orbitals that house the electrons for a given system. The electron energy functionals approximate the electron exchange and electron correlation energies for all electrons in a system. The wave function describes all spatial properties, such as momentum, kinetic energy, potential energy, etc. of the electron with respect to its position. Together, basis sets and functionals can provide an approximate electron density of the molecule, and thus provide an approximate solution to the Schrödinger equation. 4

15 2.2.1 THE EXCHANGE CORRELATION FUNCTIONAL The energy functional is a mathematical description of the total energy of a system. For a many bodied system, an approximation is necessary for the electron exchange and correlation energy components of the energy functional. The results obtained between different functionals are largely dependent on the size and geometry of the molecules being modeled. Likewise, different functionals provide different methods for calculating the exchange and correlation energies of the electrons. For example, the Hartree Fock (HF) theory uses the simple solution to the Schrödinger equation of a hydrogen atom, and multiplies additional single electron wave functions to obtain the total wave function 14, thus modeling the electron exchange exactly and omitting energetic contributions of the electron correlation energy. While the Hartree Fock method takes the approach of solving the many electron problem by directly solving with the wave function, density functional theory (DFT) instead uses the electron density as an approximation of the wave function. A basic method to approximate the exchange correlation term is known as Local Density Approximation (LDA). This method was used by Hohenburg and Kohn 15 to model a system of slowly varying density. LDA uses the exchange correlation energy of a uniform electron gas of the same density of whichever system is being modeled. The energy of true density can be approximated by the energies of the local densities. A similar approach is with Local Spin Density Approximation (LSDA), which separates out the densities associated with spin up and spin down electrons instead of dealing with them both combined. The LSDA does not have an analytic form for correlation energy, but Monte Carlo simulations have been performed to create empirical values 16. Both of these methods fail to work when there is a sharp change in electron densities. 5

16 The Generalized Gradient Approximation (GGA) and meta Generalized Gradient Approximation (meta GGA) incorporate a more sophisticated method for developing the exchange and correlation energies. Both methods correct for the LDA and LDSA methods when there is a fast change in electron density by including the gradient of the electron density. The Meta GGA approximation provides an even more accurate result than the Generalized Gradient Approximation (GGA) by including the Laplacian of the electron density, rather than just the gradient. Hybrid functionals offer a combination of DFT and HF components. In this way, the good qualities of each method can be combined to form a flexible method of approximating the exchange correlation functional 16. For example, the terms for exchange energy can incorporate a specific proportion of LDA and GGA, and the exchange component can incorporate an entirely different proportion of LDA, GGA, and HF exchange. This research focuses on the use of B3LYP, M06 2X, CAM B3LYP, and wb97xd functionals. B3LYP 17 is a hybrid functional developed by Axel D. Becke that contains a mixture of HF and LDA. The M06 2X 18 functional is classified as a hybrid meta exchange correlation functional, which uses long range corrections by doubling the non local exchange for longer ranges, but does not use LDA. CAM B3LYP 19 is a hybrid functional that combines the qualities of B3LYP while adding longrange corrections by switching the blend of 19% HF exchange at short range to 65% HF for longrange calculations. wb97x D 20 is a hybrid functional that uses empirical dispersion corrections and a damping function to correct for long range electron interactions. These functionals were selected to evaluate a range of methods for calculating electronic excitations. B3LYP is one of the most popular functionals used in current electronic excitation calculations, while the other three functionals have all been shown to perform well in these calculations When a molecule 6

17 undergoes a shift in its electron density from excitation or emission, the molecule can become polarized, and dispersion forces can start affecting the molecule. M06 2X, CAM B3LYP, and wb97xd all incorporate some form of corrections for dispersion forces THE BASIS SET A basis set is a collection of functions used to construct the atomic orbitals in the model. The electron density of a molecule is dependent on the atomic orbitals defined by the basis set. Therefore, determining the atomic orbitals is required for determining the energy in the system. In this way, the calculation of the energy of a system can be specific to each unique molecular system being modeled, as the electron density is unique to each molecular structure. In 1930, J.C. Slater published a paper 19 that determined the effective charge felt by an electron in an atomic orbital. Using this information, Slater developed a method for determining the density of electrons in their shells at different radii. Using the linear combination of atomic orbitals, the energy of the molecular orbital could then be described. This formation of a basis set is known as slater type orbitals (STO). STO are basis functions that have a direct physical interpretation to the orbits of a hydrogen atom, but are cumbersome to calculate in large models. Instead, approximations to STOs can be made through a linear combination of Gaussian type orbitals (GTO). While GTO are good at describing atomic orbitals, GTO do not allow orbitals to expand or shrink when in the vicinity of other atoms in a molecule. To aid in this deficiency, extra functions are added beyond the minimum necessary to describe each atom. In addition, the contributions from each of these additional functions can be weighted in specific ways to better approximate the wave function. Basis sets are called double zeta (in the valence electronic structure) when they contain twice as many basis functions as the minimum basis set. Basis sets are called triplezeta (in the valence electronic structure) when they contain triple as many basis functions as the 7

18 minimum basis set. Both double zeta and triple zeta basis sets are considered split valence due to the partitioning of the valence electronic structure into different functions. Additional functions can be added to these basis sets such as polarization or diffuse functions 26. Polarization functions allow atomic orbitals to become polarized and move when in the vicinity of other nearby atoms. Diffuse functions allow electrons to occupy a wider area within the same orbital than it would be defined otherwise. This research utilizes 6 31G(d,p) 27, 28 basis set for all of the calculations to balance computationally efficiency and accuracy. The 6 31G(d,p) basis set includes six GTO s to describe the core electrons, and the valence structure is split into two separate GTO s; one containing three Gaussian function, and the second containing one. There are also polarization functions added to all atoms SOLVENT MODELS DFT calculations are performed in the gas phase unless a solvation model is deliberately chosen. Solvation can be modeled explicitly or implicitly, or in the gas phase. Explicit models incorporate the solvent in the model explicitly and have the benefit of describing direct solutesolvent interactions 29. However, explicit models are time consuming, computationally intense, and difficult to perform. Alternatively, implicit models describe the solvent as a continuum, which presents the solvent as a polarizable media. Implicit solvation models are computationally simpler than explicit models, but are unable to account for specific solute solvent interactions. A popular continuum model is the polarized continuum model (PCM), which describes the solvent through a polarizable field using the dielectric constant of the chosen solvent. A cavity associated to the molecular shape of the solute molecule is inserted within the polarizable field and an apparent surface charge is expressed 29. Within the implicit domain, excitation calculations can be performed using linear response theory (LR), or state specific (SS) theory. An essential advantage 8

19 of the state specific (SS) approach compared to linear response theory (LR) is the ability of a state specific calculation to properly account for the mutual relaxation of the solute electron density and the response from the solvent during excitation. Therefore, the state specific approach has a more accurate description of the electrostatic interactions between solute and solvent molecules, leading to a more accurate determination of excitation energies 29. Calculations performed in the gas phase place the solute in the presence of no other solvents or solutes, but as a single molecule. These models use LR theory, which by default is an inferior method for calculating absorption and emission bands compared to SS methods. Due to the constraints from both purely implicit and explicit models, hybrid techniques have been developed that incorporate the explicit model at the first solvation shell, while using an implicit model to account for the bulk solvent effects. Studies have shown that modeled electronic excitations compare well with experimental work when the solvent field has explicit components This research uses a technique called Our own N Layered Integrated molecular Orbital and molecular Mechanics (ONIOM) 34 as implemented in Gaussian ONIOM is a technique that allows for assigning theory based hierarchical layers to the structures in the model. In other words, some structures in a model can be treated using highly accurate theories, such as quantum mechanical DFT/TD DFT theories, while other portions can be assigned more simple approximation such as HF exchange. This can allow for treating very large systems with up to three levels of theories to keep computational costs low while maintaining accuracy 34, 36. In this respect, the main fluor molecule can be treated with the highest level of theory, and the explicit solvent molecules can be treated with a less precise theory to save computational cost. Likewise, the entire system can then be inserted as a cavity inside of a PCM field to simulate the bulk solvent effects. Implementation of PCM in the ONIOM system can be executed using a technique called 9

20 ONIOM PCM 37. This technique performs PCM calculations on the ONIOM defined system, and has four different methods that can be chosen. ONIOM PCM/A is the most correct method, but only computes transition energies, not geometry optimizations. Instead, ONIOM PCM/X is an approximation to the ONIOM PCM/A method, and can be used for geometry optimizations CHEMICAL STRUCTURES Figures 2 4 show the chemical structures of the organic fluors used in this study 1, 2. Figure 2. Chemical structures of αnpo and vnpo. Figure 3. Chemical structures of PBD and vpbd. 10

21 Figure 4. Chemical structure of PZ1, vpz1, and PZ2. 3. METHODOLOGY DFT and TD DFT calculations were performed using Gaussian09 35 to determine the ground state and excited state geometries and energies of αnpo, vnpo, PBD, vpbd, PZ1, vpz1, and PZ2 fluor molecules using the B3LYP, M06 2X, CAM B3LYP, and wb97x d functionals and the 6 31G(d,p) 36, 37 basis set. Calculations were performed by including the excitations from the ground state up to the sixth singlet excited state. 3.1 GAS PHASE MODEL The gas phase model was executed to compare with the solvated models. The fluorescence of each fluor molecule in the gas phase was calculated using the M06 2X functional. The gas phase fluorescence calculations consists of four steps. Figure 5 presents each calculation step performed and the deliverables each step produced. 11

22 Figure 5. Flow diagram of computational steps required to complete the gas phase absorption and emission calculations. DFT theory (solid box), TD DFT (dashed box). For each optimized geometry calculation, a vibrational frequency calculation was performed to confirm that the calculation reached the minimum on the potential energy curve (Figure 5, step 1). The vibrational spectra were analyzed to confirm the absence of any negative frequencies. Negative frequencies occur if a molecular geometry is not at the energetic minimum. Once the ground state geometry is determined, the linear response excitation energy to the first excited state is calculated in the gas phase (Figure 5, step 2). The excited state geometry is calculated by perturbing the ground state geometry, injecting the excitation energy, and reoptimizing the molecule at the first excited state (Figure 5, step 3). Again, a frequency calculation is executed to confirm the geometry is legitimate, and the emission spectrum is produced (Figure 5, step 4). 3.2 IMPLICIT SOLVATION MODEL The implicit solvation model was executed by implementing the PCM technique in six steps for each molecule to model the complete absorption emission process. The six steps can be sorted into three broad categories 1) geometry optimizations, 2) transitional energy calculations, and 3) vibrational frequency calculations. For each optimized geometry calculation, a vibrational frequency calculation was performed. Figure 6 shows the progression of executed calculations (rectangles) and the associated deliverables (ovals). 12

23 Figure 6. Flow diagram of computational steps required to complete the geometry optimization, absorption, and emission calculations for PCM solvation implementation. DFT theory (solid box), TD DFT (dashed box). The first calculation performed is a DFT ground state geometry optimization with the addition of an atomic bond frequency calculation (Figure 6, Step 1). Toluene (dielectric constant (ε) = ) and cyclohexane (ε=2.0165) were selected as solvents for all molecules of interest, and chloroform (ε= ) and diethyl ether (ε= ) were selected as additional solvents for the αnpo, vnpo, and PZ1 fluors to probe the effect of an organic solvent with a larger dielectric constant than those of cyclohexane and toluene. The deliverables from this initial step include both the energetics and the vibrational frequencies of the optimized structure. TD DFT theory is used to calculate the absorption spectra of each molecule. The excitation energy required to reach the first excited state (Figure 6, Step 2) is computed and used to calculate the first excited state geometry (Figure 6, Step 4). In order to obtain a more realistic model for the absorption energy and wavelength, a state specific solvation approach is used (Figure 6, Step 3). The state specific absorption calculation will provide the wavelengths associated with the different orbital transitions, as well as the relative intensity expressed as oscillator strength. 13

24 Unlike the state specific absorption energy (Figure 6, Step 3), the energy calculated in step 2 uses the linear response theory, which does not fully represent the solvent effects, but is computationally efficient. The solvent effects that are not fully considered in the linear response calculation are corrected for later (Figure 6, Step 6). The first excited state geometry was calculated from the ground state geometry (Figure 6, Step 4) and the vertical excitation energy (Figure 6, Step 2). The ground state geometry is perturbed and the excitation energy is imposed onto the molecule, which is re optimized to find the stationary state corresponding to the first excited state. Like with the ground state optimization, a frequency calculation is performed (Figure 6, Step 5) to ensure the geometry of the excited state is at a stationary state. After necessary solvent effects are corrected for the excited state (Figure 6, Step 6), the resulting emission wavelength ( ) is computed using the Planck Einstein relationship, where, where E is the energy difference between the ground state and the energy of the molecule in the first excited state, h is Plank s constant, and c is the speed of light in a vacuum. This emission wavelength is also paired with an oscillator strength. 3.2 HYBRID SOLVATION MODEL Hybrid solvation methods were implemented on the αnpo and vnpo to test whether the presence of explicit solvents would alter the results obtained dint he implicit solvation scheme. The NPO molecules were chosen due to their relatively small structures compared to the other five fluor molecules; including explicit solvents into the model increases computational costs. Two methods were implemented to simulate the hybrid solvation. The first method used the ground state geometry of the αnpo and vnpo fluor molecules that were previously optimized with the PCM scheme as a starting point. For αnpo, a single toluene molecule was placed approximately 3 Å from the C H of the oxazole group, with the methyl group directed towards the fluor. For 14

25 vnpo, a single toluene molecule was placed approximately 3 Å from the CH 2 of the vinyl group, with the toluene methyl group directed towards vnpo vinyl group. Figure 7 demonstrates the initial coordination of the explicit toluene with respect to the αnpo and vnpo molecules. a) b) Figure 7. PCM hybrid technique showing the initial coordination of a single explicit toluene for a) αnpo and b) vnpo. This single toluene would act as a starting point to determine toluene coordination around the fluor, while the PCM model approximated the bulk solvent environment. Calculations in this method followed the same procedure outlined in Figure 6. The second method was implemented using a two layer ONIOM technique. Each fluor molecule was treated with a high level theory, i.e., the M06 2X functional and 6 31G(d,p) basis set. The explicit solvent molecules were treated more simplistically, i.e., with the HF exchange and the 6 31G(d,p) basis set. Bulk solvation effects were accounted for using the ONIOM PCM 37 technique, utilizing both the ONIOM PCM/A and ONIOM PCM/X executions. Figure 8 presents an example of the layering technique used for the αnpo molecule in toluene. 15

26 Figure 8. Two layer ONIOM technique for αnpo in toluene. M06 2X/6 31G(d,p) theory is applied to the fluor molecule, HF/6 31G(d,p) theory for interactions between the fluor molecule and explicit toluene molecules, and ONIOMPCM theory to model bulk solvation. The application of the ONIOM PCM technique for the ground state geometry optimizations was evaluated in two different ways to reduce computational cost. In the first two methods, six explicit toluene molecules were arranged around the αnpo and vnpo molecules with the average distance between the hydrogens of the toluene and the hydrogens of the αnpo and vnpo fluors being 4 Å. The ground state geometry of the fluor molecule optimized with the PCM scheme was used as a starting point, and frozen prior to optimization of the fluor with explicit solvation. For example, the starting geometry of the αnpo molecule used for the hybrid solvation method in toluene was the optimized ground state geometry in toluene from the PCM model. The geometry of the fluor molecule remains fixed, while the first coordination sphere of solvent molecules are optimized. The electron density on the fluor is still optimized, and by fixing the geometry of the 16

27 previously optimized fluor molecule, computation costs are dramatically reduced. The second method used the optimized geometry from the first method, freezing the pre optimized solvent molecules and further optimizing the fluor molecule. The linear response excitation energy was calculated using the ONIOM PCM/A technique for both the system containing a frozen fluor molecule and the system containing the frozen solvent molecules to determine the absorption spectrum. Due to the complexity of the system, emission calculations were not feasible for the hybrid solvation approach. Only steps 1 and 2 in Figure 6 were performed for the ONIOM technique calculations. 4. RESULTS 4.1 ENERGY FUNCTIONAL EFFECTS The absorption spectrum for αnpo was calculated using the B3LYP, CAM B3LYP, M06 2X, and wb97x D functionals (Figure 9) Intensity αnpo Absorption Wavelength (nm) B3LYP CAM B3LYP M062X wb97x D Figure 9. Absorption spectra for αnpo in toluene for each functional in toluene. Curves normalized to CAM B3LYP. 17

28 The B3LYP functional tends to overestimate the absorption wavelength as compared with the long range corrected functionals. Further, the long range corrected functionals show more pronounced absorption features at smaller wavelengths, and the overall intensities of the peaks are larger than those produced by the B3LYP functional. Similar results are observed for the other fluor molecules, as well (Appendix 1). Thus, the long range corrected functionals are able to identify more distinct absorption excitation pathways than the B3LYP functional. The three long range corrected functionals identify the primary absorption peak of αnpo to be nm (wb97x D), nm (M06 2X), and nm (CAM B3LYP). However, the functionals differ in the intensity of the lower wavelength features. As expected, the wb97x D and CAM B3LYP functionals perform similar to each other 24, and more so than the M06 2X functional. For the αnpo 213 nm absorption wavelength, the M06 2X functional results in an intensity roughly four times larger than the wb97x D intensity, and roughly 6.5 times larger than the CAM B3LYP intensity (Figure 10). The M06 2X performed similarly for the other absorption spectra of the remaining molecules, as seen in Appendix 1. Figure 10 shows a comparison of the calculated absorption spectra of vnpo in toluene vs. the experimental spectra obtained in methyl acetate. 18

29 1 0.8 Intensity vnpo Absorption Wavelength (nm) B3LYP CAM B3LYP M06 2X wb97x D Experimental Methyl Acetat Figure 10. Calculated vnpo absorption spectra in toluene vs experimental spectra in methyl acetate. Calculated curves normalized to wb97x D, experimental curve normalized to itself. The location of absorption features produced by the M06 2X, CAM B3LYP, and wb97x D functionals are more consistent with the experimental results than the B3LYP functional (Figure 10). The ground state to excited state absorption consists of a one electron transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). Figure 11 shows the electron density orbital projection for vnpo using the B3LYP and M06 2X functional in toluene for the first excited state transition. Orbital projections are constructed by treating electrons mathematically as waves, so therefore orbitals have phase signs. In Figure 11, the positive phase is red, while the negative phase is blue. All atoms are labeled with their atom type and number, excluding hydrogens. 19

30 Figure 11. HOMO and LUMO molecular orbitals of αnpo for B3LYP and M06 2X in toluene. The B3LYP and M06 2X energy functionals produce similar HOMO and LUMO levels (Figure 11). The electron density distribution at the HOMO level are at sites that will act as electron donors, while the electron density distribution at the LUMO level are at sites that will act as electron acceptors during excitation of electrons 38. In Figure 11, the HOMO structure has a balanced electron density stretching over C=C bonds and sharing electron density with the oxygen and nitrogen atoms. When transitioning to the LUMO structure, the electron density shifts from the vinyl group, and most of the density accumulates in the naphthyl group and on the individual oxygen and nitrogen atoms. The strength of the interaction between electron donors and electron acceptors is quantified by the magnitude of the hyper conjugative interaction energy (E (2) ) 38. Larger E (2) values represent the delocalization of electron density between occupied (bonding) and unoccupied (anti bonding) orbitals, leading to a more stabilizing donor acceptor interaction 38. As 20

31 seen in Figure 11, the transition from HOMO to LUMO levels consist mostly of transitions. Table 1 presents the transitions of interest for the vnpo molecule, based on stability energy interactions (E (2) ) greater than 10 kcal/mol. As seen in Table 1, the M06 2X energy functional produced stronger stability interaction energies (E (2) ) for every electron donor acceptor pair, leading to an overall stability that is much stronger than the interactions calculated by the B3LYP energy functional. Table 2 presents the energies associated to the HOMO and LUMO calculated by the B3LYP and M06 2X functionals, as well as the optical gap energy. The HOMO LUMO energy gap is an approximation to the fundamental electronic gap, i.e. the energy to free an electron from its bound hole between ground state and excited state levels, while the optical gap is the energy gap required to excite a bound electron to an excited state with a photon. Larger HOMO LUMO gaps represent a more stable molecule during chemical reactions 38. Larger optical gaps require higher energy photons (shorter wavelength) to excite electrons from the ground state to the first excited state. 21

32 Table 1. Donor and Acceptor Orbitals and Corresponding Interaction Energies (kcal/mol) of the vnpo Fluor Molecule Calculated Using B3LYP/6 31G(d,p) and M06 2X/6 31G(d,p) Energy Functionals in Toluene. E (2) (kcal/mol) Donor Acceptor B3LYP M06 2X π(c1 C2) π*(c3 C4) π(c1 C2) π*(c5 C6) π(c3 C4) π*(c1 C2) π(c3 C4) π*(c5 C6) π(c5 C6) π*(c1 C2) π(c5 C6) π*(c3 C4) π(c5 C6) π*(c12 C13) π(c12 C13) π*(c5 C6) π(c12 C13) π*(c14 N16) π(c12 C13) π*(c34 C36) π(c14 N16) π*(c12 C13) π(c17 C22) π*(c18 C19) π(c17 C22) π*(c20 C21) π(c18 C19) π*(c17 C22) π(c18 C19) π*(c20 C21) π(c18 C19) π*(c26 C30) π(c18 C19) π*(c28 C32) π(c20 C21) π*(c14 N16) π(c20 C21) π*(c17 C22) π(c20 C21) π*(c18 C19) π(c26 C30) π*(c18 C19) π(c26 C30) π*(c28 C32) π(c28 C32) π*(c18 C19) π(c28 C32) π*(c26 C30) π(c34 C36) π*(c12 C13) a LP(2)O15 π*(c12 C13) a LP(2)O15 π*(c14 N16) a LP(1)N16 σ*(c14 C20) ΔE (π > π*) kcal/mol ΔE (LP > π*) kcal/mol ΔE (LP > σ*) kcal/mol TOTAL ΔE kcal/mol a LP(x) represents a lone pair, and the x electron of that pairing. 22

33 Table 2. Calculated HOMO, LUMO, HOMO LUMO Gap, and Optical Gap Energies Using B3LYP/6 31G(d,p) and M06 2X/6 31G(d,p) in Toluene. Calculated Energy (ev) Functional HOMO LUMO HOMO LUMO Gap Optical Gap B3LYP M06 2X From Table 2, the M06 2X calculated a more stable HOMO, which is validated by the larger stability energies presented in Table 1. However, the B3LYP predicts a more stable LUMO structure, resulting in a smaller HOMO LUMO gap. This means that the transition from HOMO to LUMO takes less energy than the transition calculated by M06 2X, and is therefore calculated to be less stable with B3LYP. There is also a difference between B3LYP and M06 2X as reflected in the optical gap. A lower optical gap energy results in the absorption peak calculated by B3LYP being at a longer wavelength than the M06 2X (Figure 11). The difference in LUMO energies between B3LYP and M06 2X can be explained by the switching bond ordering in the naphthyl group, as demonstrated in Table 3. In the ground state HOMO structure, both B3LYP and M06 2X calculated the same locations of C=C double bonds in the naphthyl group. At the LUMO level, the B3LYP energy functional did not change the conjugation order of the C=C double bonds in the naphthyl group, but the M06 2X did. As a result, the M06 2X excited state structure consists of three consecutive single C C bonds between C18 C 28, C18 C 19, and C 19 C26. By disrupting the conjugation order of alternating double and single carbon bonds, the excited state structure calculated by M06 2X is less stable than the structure calculated by B3LYP. As a result of a strong HOMO level and weaker LUMO level, the calculated HOMO LUMO gap is larger using M06 2X than when calculated using B3LYP. 23

34 Table 3. Comparison of Bonding Order Between the HOMO and LUMO States Calculated Using B3LYP and M06 2X Functionals. HOMO LUMO Bonding B3LYP M06 2X B3LYP M06 2X Type Orbitals Type Orbitals Type Orbitals Type Orbitals C1 C2 Double π Double π Double π Double π C3 C4 Double π Double π Double π Double π C5 C6 Double π Double π Double π Double π C12 C13 Double π Double π Double π Double π C14 N16 Double π Double π Double π Double π C17 C22 Double π Double π Double π Single σ C18 C19 Double π Double π Double π Single σ C20 C21 Double π Double π Double π Single σ C26 C30 Double π Double π Double π Double π C28 C32 Double π Double π Double π Double π C34 C36 Double π Double π Double π Double π O15 LP(2) π LP(2) π LP(2) π LP(2) π N16 LP(1) LP LP(1) LP LP(1) LP LP(1) LP C20 a a a a a a LP(1) π a Bond not present in structure. Based on the inconsistent calculations of B3LYP to properly describe the electronic and optical transitions occurring in the fluor molecules, the M06 2X functional was used for the remaining calculations to evaluate the implicit and hybrid solvation models. The M06 2X functional has been consistent with other long range functionals, and has been recommended for electronic excitation calculations IMPACT OF SOLVATION GAS PHASE VS IMPLICIT SOLVATION Table 4 presents the location of the M06 2X/6 31G(d,p) calculated primary absorption wavelength and oscillator strength, emission wavelength, and corresponding Stokes Shift of each fluor molecule using the gas phase linear response (LR) theory, the PCM LR theory in toluene, and the PCM state specific (SS) theory in toluene. Oscillator strengths express the probability of 24

35 absorption, with higher oscillator strengths equating to more probable absorption. Stokes Shifts are the difference between emission and absorption wavenumbers. Table 4. The Absorption and Emission Wavelengths λ (nm), Oscillator Strengths (f), and Stokes Shifts Δν (cm 1 ) of Gas Phase Linear Response (Gas Phase), PCM Linear Response (PCM LR) in Toluene, and PCM State Specific (PCM SS) in Toluene for Each Fluor Molecule Using M06 2X/6 31G(d,p). Fluor Method Absorption Emission λ A (nm) f λ E (nm) Δν (cm 1 ) b Gas Phase αnpo PCM LR PCM SS Gas Phase vnpo PCM LR PCM SS Gas Phase PBD PCM LR PCM SS Gas Phase vpbd PCM LR PCM SS Gas Phase PZ1 PCM LR PCM SS Gas Phase a a vpz1 PCM LR PCM SS Gas Phase a a PZ2 PCM LR a a PCM SS a a a No data available. b Δν (cm 1 ) = 1/ λ A 1/ λ F The transition from the gas phase to the solvated models results in a red shift in the absorption and emission wavelengths (Table 4). The PCM SS absorption wavelength is represented more consistently by the gas phase LR wavelength for the αnpo, PBD, and vpbd fluors with respect to the wavelengths and oscillator strengths, while the PCM LR wavelength 25

36 most accurately approximates the PCM SS wavelength for the vnpo, PZ1, vpz1, and PZ2 molecules, but not the oscillator strengths. Both the gas phase LR and PCM LR overestimate the intensity of the absorption peaks compared to the PCM SS scheme, but the gas phase LR is closer to the intensity of the PCM SS scheme than the PCM LR. The gas phase absorption intensities are more similar to the PCM SS absorption intensities than the PCM LR absorption intensities are, which are larger in magnitude. The trends in the emission spectra are similar to the trends observed in the absorption spectra, in which the PCM LR scheme over predicts the intensity with respect to the PCM SS, while the gas phase LR is of the same relative intensity SOLVENT EFFECTS In real systems, the absorption spectra recorded in solvents of different polarity result in different wavenumbers and intensities 39. Likewise, emission bands typically experience a redshift in wavenumber when polarity is increased 39, 40. A comparison of the primary absorption and emission wavelengths for each fluor molecule in cyclohexane and toluene solutions using the M06 2X functional is presented in Figure 12. Emission wavelengths could not be calculated vpz1 in cyclohexane, nor for PZ2 in cyclohexane and toluene, as the excited state geometry could not be determined. The tabulated data is available in Table 10, Appendix 1. 26

37 Wavelength (nm) Absorption Emission Absorption Emission Absorption Emission Absorption Emission Absorption Emission Absorption Emission Absorption Emission αnpo vnpo PBD vpbd PZ1 vpz1* PZ2* Cyclohexane Toluene Figure 12. First excited state absorption peak location for each fluor molecule in cyclohexane and toluene, using M06 2X/6 31G(d,p). *No data available. The location of absorption and emission peaks are almost identical for each fluor in toluene and cyclohexane solutions (Figure 12). Likewise, there is no consistent pattern of which solvent produces a larger absorption or emission wavenumber between the fluors. The maximum difference in absorption wavelength for the different solvents occurs for PZ1, which produces an absorption wavelength 1.99 nm higher in toluene than in cyclohexane. The maximum difference in emission wavelength occurs for vnpo, which produces an emission wavelength 2.28 nm higher in toluene than in cyclohexane. The full absorption and emission spectra of each fluor in toluene solution can be seen in Appendix 1. 27

38 The variation in absorption and emission peak intensities of each fluor molecule in toluene and cyclohexane is presented in Table 5, which shows the percent difference between intensities obtained in cyclohexane and toluene for the three most prominent absorption pathways, and the emission from the first excited state observed in the spectrum (in descending order). The percent difference is expressed by: (2) Table 5. Percent Differences of the Intensities of the Three Most Prominent Absorption Transitions, Their Corresponding Wavenumber (λ), and the Emission Peaks from the First Excited State of Each Fluor Molecule in Toluene and Cyclohexane Solutions using M06 2X/6 31G(d,p). Absorption Emission Percent Difference of Peak Intensities Fluor Excited State λ A (nm) Excited State λ E (nm) Absorption Emission % αnpo % 0.06% % % vnpo % 0.13% % % PBD % 0.03% % % vpbd % 0.11% % % PZ % 1.41% % % vpz a 2.50% a % % PZ a 1.13% a % a Data not available to perform comparison. 28

39 Table 5 shows that the most significant difference in the excited state 1 absorption pathway occurs for the vnpo molecule, with an absorption intensity in cyclohexane 2.01% higher than in toluene. Likewise, the vpz1 molecule was the only fluor in which the first excited state absorption pathway recorded a higher intensity in toluene than in cyclohexane. The most significant difference in emission peak intensities occurs for the PZ1 molecule, with an intensity in toluene 1.41% higher than in cyclohexane. The PCM model predicted the excitation to the first excited state as the primary absorption pathway for all of the fluor molecules, but the second and third most probable excitation pathways between fluors of similar structure varied. The model predicted that αnpo would have an excitation pathway to the third excited state as more probable than the sixth excited state, while vnpo was predicted to preferentially absorb to the sixth excited state rather than the third. This is interesting, because along with αnpo, the PBD and vpz1 fluors all predicted that the second most probable excitation pathway was at a wavelength lower than the third most probable pathway. This is interesting because the energy required to absorb at these wavelengths is larger than the next most probable absorption pathway. However, the difference between solvents is small, as the largest percent difference between the second most probable absorption pathway and third most probable pathway was 3.71% and 2.42%, respectively. Thus, the implicit solvation approach (PCM implementation) does not produce significant absorption and emission wavelength differences, nor intensity differences between the cyclohexane and toluene solvents. Even the secondary and tertiary absorption pathway differences are low in magnitude. This may be due to the similarity of polarity between toluene and cyclohexane as defined by their dielectric constant ( and , respectively). Figure 29

40 13 15 show a comparison of the calculated absorption and emission spectra for αnpo, vnpo, and PZ1 in toluene, cyclohexane, chloroform, and diethyl ether using M06 2X/6 31G(d,p) Intensity αnpo Wavelength(nm) Chloroform Cyclohexane Diethyl Ether Toluene Figure 13. αnpo absorption (solid) and emission (dashed) spectra in chloroform, cyclohexane, diethyl ether, and toluene using M06 2X/6 31G(d,p). Spectra normalized to emission spectrum of diethyl ether Intensity vnpo Wavelength (nm) Chloroform Cyclohexane Diethyl Ether Toluene Figure 14. vnpo absorption (solid) and emission (dashed) spectra in chloroform, cyclohexane, diethyl ether, and toluene using M06 2X/6 31G(d,p). Spectra normalized to emission spectrum of diethyl ether. 30

41 1 0.8 Intensity PZ1 Wavelength (nm) Chloroform Cyclohexane Diethyl Ether Toluene Figure 15. PZ1 absorption (solid) and emission (dashed) spectra in chloroform, cyclohexane, diethyl ether, and toluene using M06 2X/6 31G(d,p). Spectra normalized to absorption spectrum of diethyl ether. These figures show that solvents with varying dielectric constants produce variations in the absorption and emission spectra. Fluors in chloroform (ε= ) and diethyl ether (ε= ) solvents produced absorption and emission spectra different from spectra produced in cyclohexane and toluene. The polarity of the solvent affects the intensity of the 213nm higher energy absorption peak, but leaves the primary absorption peak relatively the same (Figure 13). On the other hand, Figure 14 shows that the polarity of the solvent has a more noticeable impact on the primary absorption peak, and less on the higher energy absorption features. This would be an indication that the ground state structure of vnpo is more polar than αnpo. The emission spectrum of PZ1 is altered more with respect to intensity than it is in wavelength, with the primary emission peaks of chloroform and diethyl ether being roughly 4% higher in intensity than those of toluene and cyclohexane (Figure 15). All three emission spectra in Figures are consistent with the expectation that increasing solvent polarity will produce a redshift in emission wavelength 39, 40. Comparable to the results for cyclohexane and toluene in Table 5, the difference 31

42 in chloroform and diethyl ether spectra are minuscule. The largest wavenumber difference between chloroform and diethyl ether occurs for the absorption spectrum of the PZ1 fluor, in which chloroform absorbed at a wavelength 1.25 nm larger than diethyl ether. The largest difference in wavenumber for emission occurred for vnpo, in which the chloroform emitted at a wavenumber 0.79 nm larger than diethyl ether. These results suggests that the PCM scheme is properly accounting for electrostatic forces between the solute and solvent, as polarity does affect the absorption and emission spectra, but the PCM scheme is not capturing solute solvent chemical interactions HYBRID SOLVATION Hybrid solvation methods incorporate the use of explicit solvent molecules and implicit solvent fields, such as the PCM method. Explicit molecules are used to model the chemical interactions of solute solvent molecules, while the implicit models can simulate bulk solution effects. The αnpo and vnpo fluor molecules were calculated using two different hybrid techniques in toluene. This first method was performed using the framework of the PCM SS method as described in Figure 6. The ground state geometries of the αnpo and vnpo fluor molecules that were previously optimized with the PCM scheme were used as a starting point. For αnpo, a single toluene molecule was placed approximately 3 Å from the C H of the oxazole group, with its methyl group directed towards the fluor. For vnpo, a single toluene molecule was placed approximately 3 Å from the CH 2 of the vinyl group, with its methyl group directed towards the vinyl group. The second method was performed using the two layer ONIOM approach, defining six explicit toluene molecules at the HF level of theory. Within the ONIOM method, two approximations were tested. First, the fluor molecule was held static during the optimization to the ground state geometry. The fluor molecule was previously optimized in the absence of an 32

43 explicit solvent. Fixing the geometry of the fluor molecule while optimizing the explicit solvent molecules enables the convergence of this large complex system. The second approximation built upon method 2, by letting the fluor molecule optimize while holding the explicit toluene static. Figures 16 and 17 report the absorption spectra obtained for the αnpo and vnpo molecules using the hybrid methods as they compare to the M06 2X/6 31G(d,p) PCM state specific method Intensity αnpo Absorption Wavelength (nm) PCM PCM Hybrid Static Fluor Static Toluene Figure 16. Absorption spectra for αnpo with PCM SS, hybrid solvation using PCM hybrid, and ONIOM two layer with static fluor and static toluene approximations. Spectra normalized to PCM SS spectrum. 33

44 1 0.8 Intensity vnpo Absorption Wavelength (nm) PCM PCM Hybrid Static Fluor Static Toluene Figure 17. Absorption spectra for vnpo with PCM SS, hybrid solvation using PCM hybrid, and ONIOM two layer with static fluor and static toluene approximations. Spectra normalized to PCM SS spectrum. The two hybrid methods produced varying results from each other (Figures 16, 17). The ONIOM two layer technique produced primary absorption peaks consistent with the implicit PCM model, but the static fluor approximation produced a higher intensity at the higher energy peak for αnpo and a different absorption feature at higher energy absorption for vnpo. In Figure 16, The PCM hybrid method produced an absorption spectrum dissimilar to the static fluor approximation, with the high energy absorption peak at 213 no longer a probable absorption band. Likewise, the entire spectrum is redshifted and lower in intensity, with the primary peak of the PCM hybrid method only 81% of the PCM SS absorption band. In Figure 17, the PCM hybrid method has an absorption spectrum more in line with the ONIOM static fluor spectrum, where the two lower absorption peaks predicted by the PCM SS method are consistent in shape, but there is a loss of the higher energy feature as seen in the PCM SS and ONIOM static toluene systems. Similar to the αnpo PCM hybrid spectrum, the entire vnpo PCM hybrid spectrum is also 34

45 redshifted and lower in intensity, with the primary peak of the PCM hybrid method 92% the intensity of the PCM SS absorption band. Figures 18 and 19 present the comparison absorption and emission bands of the αnpo and vnpo fluor molecules using the implicit PCM and PCMhybrid techniques Intensity Wavelength (nm) PCM PCM Hybrid Figure 18. αnpo absorption (solid line) and emission (dashed) spectra calculated using implicit PCM and PCM hybrid models and M06 2X/6 31G(d,p). Spectra normalized to PCM emission Intensity Wavelength (nm) PCM PCM Hybrid Figure 19. vnpo absorption (solid line) and emission (dashed) spectra calculated using implicit PCM and PCM hybrid models and M06 2X/6 31G(d,p). Spectra normalized to PCM emission. 35

46 The primary absorption wavelength of both αnpo and vnpo experienced a redshift from nm to nm, and nm to 319 nm respectively (Figures 18, 19). Additionally, the oscillator strength decreased from 0.66 to 0.54 for αnpo and 0.55 to 0.51 for vnpo. The emission bands of both αnpo and vnpo did not experience as drastic of a redshift as the absorption, but increased from nm to nm, and to nm respectively. This results in a Stokes Shift of and nm, which is 6.39 nm and 8.01 nm shorter than the implicit model predicts. Similarly, the intensity was less than the implicit PCM model by 29% for αnpo and 14% for vnpo, but both emission bands were still higher than their respective absorption intensity. Tabulated data comparing the hybrid methods and PCM SS in toluene can be seen in Table 6. Table 6. Absorption and Emission Wavelengths λ (nm), Oscillator Strengths f, and Stokes Shifts Δν (cm 1 ) of αnpo and vnpo Fluor Molecules Calculated by Hybrid Solvation and the PCM SS Method Using M06 2X/6 31G(d,p) in Toluene. Calculated Fluor Method Absorption Emission λ A (nm) f λ E (nm) a Δν (cm 1 ) PCM SS αnpo Static Fluor b b Static Toluene b b PCM Hybrid PCM SS vnpo Static Fluor b b Static Toluene b b a Δν (cm 1 ) = 1/ λ A 1/ λ F b Data not available PCM Hybrid

47 From Table 6, the results from the PCM hybrid technique did alter the absorption and emission wavelengths of αnpo and vnpo, and also magnitudes differentiating the two. In the PCM SS model, the vnpo fluor absorbed at a wavelength 3.43 nm more than αnpo, and also emitted at a wavelength 3.85 nm larger, which resulted in a Stokes Shift of vnpo only 0.42 nm higher than αnpo. In the PCM hybrid model, the vnpo fluor absorbed at a wavelength only 2.5 nm more than αnpo, and also emitted at a wavelength 1.20 nm larger, which resulted in a Stokes Shift of vnpo being only 1.20 nm shorter than the αnpo fluor, reversing the trend. The results from the implicit solvation model can be used to compare the absorption and emission spectra of the fluor molecule. 5. CHEMICAL EFFECTS Figure 20 presents the absorption spectra of each fluor in toluene calculated using the M06 2X functional as well as experimental absorption spectra of each fluor molecule in methyl acetate. 37

48 Intensity Absorption Wavelength (nm) αnpo vnpo PBD vpbd PZ1 vpz1 PZ2 Absorptivity Absorption Wavelength (nm) αnpo vnpo PBD vpbd PZ1 vpz1 PZ2 Figure 20. Top: Calculated absorption spectra of each fluor molecule using the PCM state specific model in toluene and M06 2X/6 31G(d,p). Spectra normalized to calculated vpbd spectra. Bottom: Experimental absorption spectra of each fluor molecule in methyl acetate. Spectra normalized to experimental vpbd spectra. The difference in molecules with or without a vinyl functional group varies with the organic molecule. The calculated primary absorption wavelength of vnpo extends to nm from the nm αnpo wavelength, but the peak is 85.82% the strength of αnpo (Figure 20). The absorption behavior for the other fluor molecules varies more significantly in both peak 38

49 position and absorptivity. The experimental primary absorption peak of vnpo and αnpo are the same, and the absorptivity of vnpo is 97% the intensity of αnpo. The calculated primary absorption wavelength of vpbd changes to nm from nm recorded for PBD, an nm difference. The calculated peak absorption intensity for vpbd is 19% higher than the calculated peak absorption intensity for PBD. In addition, the experimental absorption wavelength of vpbd changed to 315 nm from the 305 nm absorption of PBD, a 10 nm difference. Additionally, the vpbd absorptivity is 19% larger than the absorptivity of PBD. The addition of the vinyl group to PBD results in an increase of the absorption wavelength and its absorptivity, while maintaining the peak location and intensities for both the model and the experimental spectra. The calculated primary absorption wavelength of vpz1 changes to nm from the nm recorded for PZ1, and its peak is 99.52% the intensity of PZ1 (Figure 20). The spectra begins to vary significantly at 275 nm and below, but the addition of the vinyl group does not have as large of an effect on the entire spectra as it did with the NPO material. PZ2, which contains a fluorine atom instead of the bromine in PZ1, records a calculated peak absorption wavelength at nm and intensity of % of the intensity of PZ1. Thus, the substitution of the fluorine (PZ2) for bromine (PZ1) has a larger impact on the absorption properties than the addition of a vinyl group (vpz1). The experimental absorption of PZ1, vpz1, and PZ2 all record the same absorption wavelength. But, the peak intensity of PZ2 is 13% higher than PZ1, and 33% higher than vpz1. These results suggest the engineered differences in PZ materials affects the intensity of the absorption peak, and not the wavenumber. Figure 22 presents a comparison of the HOMO and LUMO of αnpo and vnpo fluors in toluene. 39

50 Figure 21. HOMO and LUMO molecular orbitals of αnpo and vnpo in toluene. αnpo and vnpo exhibit similar HOMO and LUMO levels (Figure 21). In the HOMO, both αnpo and vnpo contain the same bonding pattern and location of π orbitals. The αnpo has a lower energy HOMO level, with energy of 6.78 ev compared to the 6.68 ev energy of vnpo. When transformed to the LUMO, the vnpo fluor has no electron density on the vinyl group and the αnpo molecule has no electron density on the C13 H bond. The αnpo has an energy of 0.83 ev, compared to the 0.86 ev LUMO of vnpo. As a result, the energy gaps for αnpo and vnpo are 5.95 ev and 5.82 ev, respectively. Figure 22 presents a comparison of the HOMO and LUMO of PBD and vpbd fluors in toluene. The HOMO and LUMO of PBD and vpbd are different due to the addition of the vinyl group in vpbd (Figure 22). The vinyl group in vpbd contains electron density in both the HOMO and LUMO orbitals, showing that electron density migration from the vinyl group does not occur 40

51 to the same degree as in vnpo. In the HOMO, PBD has an energy of 7.26 ev and an energy of 0.86 ev in the LUMO, resulting in a HOMO LUMO gap of 6.40 ev. vpbd has a HOMO structure of 7.08 ev and a LUMO structure of 0.98 ev, leading to a HOMO LUMO gap of 6.10 ev. Figure 23 shows a comparison of the HOMO and LUMO of PZ1, vpz1, and PZ2 fluors in toluene. 41

52 Figure 22. HOMO and LUMO molecular orbitals of PBD and vpbd in toluene. 42

53 Figure 23. HOMO and LUMO molecular orbitals of PZ1, vpz1, and PZ2 in toluene. 43